The ending -ить does not tell you much about how a verb is conjugated. As you've seen, verbs ending in -ить can be conjugated differently. Let me throw in:
люби́ть - люблю́
жить - живу́
Note that бре́ю and гнию́ also differ in emphasis.
Moreover, verbs that are conjugated similarly, can have different infinitives:
брею, бреешь, бреет, INFINITIVE: брить
Горячее, as a noun, refers to a particular dish — usually a meat dish.
Я люблю есть горячее. (meaning "I like eating hot meat dishes")
Принесли горячее – жаркое со свининой.
And for the adjective горячее, you need a noun in the sentence or in the context (and the meaning is different, referring to the temperature, or the way the dish is served).
Что in this context is a relative pronoun, corresponding to English "who", "that" or "which".
If those professors that teach the students…
There also was Lena, the lead singer, who was a grade younger
You (literally, "that (woman)"), who were with me, where are you now?
This usage is a little bit dated, and a ...
As a rule of thumb, the perfective form refers to a completed action, while imperfective form implies that the action was in progress (and not necessarily finished). However, in real life there are a lot of nuances :-). Let's just look at your particular examples:
Example 1:"я видел его вчера" vs "я увидел его вчера"
The above-referenced ...
Generally, perfective forms are used for singular, novel events, while imperfective forms are used for events that might have occurred repeatedly.
"я видел его вчера" - "I saw him yesterday". "я увидел его вчера" - "I was successful (or lucky) in seeing him yesterday";
"он звонил мне вчера" - "He ...
The phrase я люблю есть горячим means "I like eating while my body temperature is high" (literally, "I like eating while I'm hot").
Note that in Russian, unlike English, the phrase я горячий doesn't mean "I'm sexy" or "I'm feeling hot". It only means what it says on the tin, like "I'm tall" or "I'm black&...
This part of Russian is one of the most problematic for foreign learners. (It's comparable to English articles, which are generally hard to explain.)
There's a class of actions which are hard to attribute completeness to. For "buy" it's clear: it's just "have bought". But what about "see", "think", "consider",...